1. **State the problem:** Expand the expression $$6a (5a - 8b - 1)$$. 2. **Formula used:** To expand, use the distributive property: $$x(y + z + w) = xy + xz + xw$$. 3. **Apply distributive property:** Multiply $$6a$$ by each term inside the parentheses: $$6a \times 5a = 30a^2$$ $$6a \times (-8b) = -48ab$$ $$6a \times (-1) = -6a$$ 4. **Write the expanded expression:** $$30a^2 - 48ab - 6a$$ 5. **Explanation:** We multiplied each term inside the parentheses by $$6a$$, keeping track of signs and variables. **Final answer:** $$30a^2 - 48ab - 6a$$